According to the rules on the US embassy website, the answer is 'yes'. (Anyone who has eve been arrested, even if completely innocent is ineligible to use the Visa Waiver Program).
http://www.usembassy.org.uk/cons_new/visa/niv/ add_crime.html
Applying for a visa is expensive, inconvenient (you have to attend an interview in London) and time-consuming (it can take many months). In practice, most people simply 'forget' about their convictions and enter under the Visa Waiver Program anyway. To do so, you should use the Electronic System for Travel Authorization (ESTA), here:
http://tinyurl.com/applyesta
Chris